Factor each polynomial completely. look for identities and expanded binomials.
8 ) 1000 a ^3 + 27 ^3
a^3 +b^3 = a^3+ ab^2 −a^2b +b^3+ a^2b −ab^2
=a(a^2+b^2−ab) + b(a^2+b^2−ab)
=(a+b)(a^2+b^2−ab)
Now a = 1000 , b= 27
1000 a ^3 + 27 ^3 = ( 1000 + 27 ) ( 1000^2 + 27 ^2 - 1000( 27 ))
= ( 1027 ) ( 1000000 + 729 - 27000)
= 1027 x 973729
= 1,000,019, 683